We have good records of impact levels on the Moon, Mars and Jupiter (although Jupiter is a little weird).
Ćirković, Sandberg & Bostrom refer to these briefly in the paper, but seem to think they're not adequate or as relevant:
For instance, the asteroidal and cometary impact history of the solar system is, in theory, easier to obtain for the Moon, where the erosion is orders of magnitude weaker than on Earth. In practice, this is still not feasible for obtaining the fair sampling of the impactors because: (1) precise dating of a large set of lunar craters is beyond our present capacities and (2) most of the large lunar craters are known to originate in a highly special epoch of the so-called Late Heavy Bombardment, ca. 4.0-3.8 billion years B.P., thus strongly skewing any attempt to plot the empirical distribution function of impacts for "normal" times. In practice, in the current debates about the rates of cometary and asteroidal impacts, it is the terrestrial cratering rates that are used as an argument for or against the existence of a dark impactor population, thus offering a good case on which the anthropic model bias can, at least potentially, be tested. [Footnote & endnote references omitted.]
From a paper by Milan M. Ćirković, Anders Sandberg, and Nick Bostrom:
There cannot have been a large disaster on Earth in the last millennia, or we wouldn't be around to see it. There can't have been a very large disaster on Earth in the last ten thousand years, or we wouldn't be around to see it. There can't have been a huge disaster on Earth in the last million years, or we wouldn't be around to see it. There can't have been a planet-destroying disaster on Earth... ever.
Thus the fact that we exist precludes us seeing certain types of disasters in the historical record; as we get closer and closer to the present day, the magnitude of the disasters we can see goes down. These missing disasters form the "anthropic shadow", somewhat visible in the top right of this diagram:
Hence even though it looks like the risk is going down (the magnitude is diminishing as we approach the present), we can't rely on this being true: it could be a purely anthropic effect.